You say left stick Y-axis, then show the right one acting up in Windows and Gamepad tester on both axis.
For RSY issues, C23 is one suspect, could try removing it and test for awhile. After that the RSY line pretty much makes a straight shot to the SOC board. Could be an iffy via in that trace, solder joint on the SOC board or the BGA joint on the MCU. Could be the MCU has some internal issue that only shows up when it's warmed up also. A shot of freeze spray, or air duster turned upside down, while it's acting up could help to see where the issue is.